Reverse bases

Find two digits \(a\) and \(b\) such that \(ab\) in base 10 is equal to \(ba\) in base 4.
Find two digits \(c\) and \(d\) such that \(cd\) in base 10 is equal to \(dc\) in base 7.
Find two digits \(e\) and \(f\) such that \(ef\) in base 9 is equal to \(fe\) in base 5.

Show answer & extension

Tags: numbers, bases
If you enjoyed this puzzle, check out Sunday Afternoon Maths VII,
puzzles about bases, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


bases colouring probability time median spheres triangles perfect numbers indices arrows surds planes prime numbers polygons coins chess odd numbers calculus functions factorials numbers symmetry shape the only crossnumber dates shapes crosswords means hexagons cards cube numbers rugby circles ellipses balancing combinatorics taxicab geometry quadratics chalkdust crossnumber chocolate cryptic crossnumbers dice geometry partitions crossnumbers mean multiplication grids multiples square roots doubling area lines addition percentages 2d shapes 3d shapes wordplay books elections fractions trigonometry menace pascal's triangle sport sequences complex numbers squares volume quadrilaterals clocks ave regular shapes integers triangle numbers rectangles probabilty averages logic folding tube maps cryptic clues scales star numbers perimeter sum to infinity speed gerrymandering tiling products dodecagons graphs digital clocks floors proportion games differentiation advent integration digits crossnumber remainders palindromes dominos money square numbers division coordinates people maths range parabolas factors unit fractions christmas sums routes algebra irreducible numbers number angles


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021